Nonlinear acoustic wave propagating in one-dimensional layered system

The propagation of finite-amplitude plane sound in one-dimensional layered media is studied by the extended method of transfer matrix formalism. For the periodic layered system consisting of two alternate types of liquid, the energy distribution and the phase vectors of the interface vibration are computed and analyzed. It is found that in the pass-band, the second harmonic of sound wave can propagate with the characteristic modulation.     

Some effects of tyre tread and road surface on road noise

A complex dynamic system can often be modeled in terms of coupled basic dynamic systems. A basic dynamic system is a system whose response can be specified in terms of a scalar quantity. A general formalism, dealing with the response of a complex dynamic system, is developed. The formalism spans several previous formalisms and encompasses new material that has not been previously considered, e.g., direct couplings between the ribs on a panel. The format is chosen so that it provides for consideration of elements of the statistical energy analysis (SEA). Thus, for example, the expression for the frequency spectral power flow between two basic dynamic systems is derived and cast in a modal form. In particular, various conditions and approximations under which cross modal terms vanish in the expression are specified and interpreted. Modal densities are defined and used to obtain further reductions in the expression for the power flow between two multimodal basic dynamic systems.     

Response of multiple coupled dynamic systems

Analytical procedures are developed to investigate the nature of the response of multiple coupled dynamic systems. The dynamic systems are one-dimensional and are coupled at junctions. The spatial extents of the dynamic systems are determined by these junctions; a dynamic system terminates at these junctions. The junctions are characterized by assigning reflection and transmission coefficients at the terminal positions of the dynamic systems. In addition, a dynamic system is characterized by a single propagation wavenumber. The wavenumber may be complex, accounting for possible spatial attenuation and for distributed damping in the dynamic system. Further damping—edge damping—may be accounted for by assigning non-conservative coefficients at the junction. Quadratic forms describing the dynamics of multiple coupled dynamic systems are also presented and discussed. Relationship of such forms to the statistical energy analysis (SEA) of complex dynamic systems is touched upon. This paper is concerned chiefly with the development of analytical procedures. Examples of application of these procedures will be dealt with in subsequent publications.     

A DESCRIPTION OF THE THERMO-ELASTIC RESPONSE OF LAYERED MEDIA BY A MATRIX FORMALISM

A matrix formalism is introduced here for the analytical calculation of the thermo-elastic response of one-dimensional optically inhomogeneous layered structures exposed to the periodic laser heating. The multilayer structure consists of thermally and mechanically homogeneous solid layers which can be interleaved by liquid ot galore interlayers. The method enables the modelling of photoacoustic and photothermal measurements in a variety of engineering applications.     

转移矩阵理论及其在Ⅲ/Ⅴ族半导体量子阱体系中的应用

应用转移矩阵方法求解三种不同量子阱体系中基于单带有效质量模型和包络函数近似下的一维定态薛定谔方程.首先,通过比较Ⅰ型单量子阱GaAlAs/GaAs/GaAlAs体系的解析解和数值解,该方法的精确性得到了验证.其次,与Ⅱ型断代量子阱AlSb/InAs/GaSb/AlSb系统的光致发光谱实验结果比较证实了该方法的适用性.最后,利用该方法推广计算了基于GaAs/GaAlAs材料的Ⅰ型耦合多量子阱体系的子带能级和波函数,说明了方法的通用性和实用性. 关键词： 量子阱 转移矩阵方法 光致发光     

广义反透射系数的物理意义

一种体系化的高效率的算法被广泛应用于分层均匀介质中有源波动方程的数值计算,它能够计算出所考察时间窗内的全波震相;该算法的关键之处,便是应用了广义反透射系数方法,广义反透射系数包含所有层间分界面反透射波及转换波的影响.本文利用图示及级数展开方法,对其物理含义进行了较为深入的分析,这对于更好地理解理论波场的合成,有较好的参考意义.     

A low diffusion particle method for simulating compressible inviscid flows

A new particle method is presented for the numerical simulation of compressible inviscid gas flows, through procedures which involve relatively small modifications to an existing direct simulation Monte Carlo (DSMC) algorithm. Implementation steps are outlined for simulations involving various grid geometries and for gas mixtures comprising an arbitrary number of species. The proposed method is compared with other numerical schemes through a series of one-dimensional and two-dimensional test cases, and is shown to provide a significant reduction in both artificial diffusion and statistical scatter effects relative to existing DSMC-based equilibrium particle methods.     

Theories of electrons in one-dimensional disordered systems

A critical survey of the literature on the theory of electronic states in, and electron transmission through, models of one-dimensional disordered solids and liquids is given in the first part. Reference to work on three-dimensional systems is included, especially where exact results have been obtained. The relationship between this subject and the problem of elastic vibrations in disordered solids is pointed out. A complete exposition of the authors' work on one-dimensional conductivity is then presented. It provides a rigorous solution of the problem of average resistance, and of the variance (fluctuations) of resistance, for important classes of disorder which are carefully and precisely defined. Conclusions regarding the role of disorder with respect to the transmission properties are presented and discussed. It is also pointed out that, with appropriate modifications, the results apply generally to wave propagation in inhomogeneous media.     

Augmented versions of the HLL and HLLC Riemann solvers including source terms in one and two dimensions for shallow flow applications

Shallow water flows are found in a variety of engineering problems always dominated by the presence of bed friction and irregular bathymetry. These source terms determine completely the possible evolution of the flooded area in time. It is well known that appropriate numerical schemes for this type of flows must be well-balanced. Well-balanced numerical schemes are based on the preservation of cases of quiescent equilibrium over variable bed elevation. Commonly they are formulated as an adaptation of numerical solvers defined for cases without source terms. This procedure is insufficient when applied to real situations. Then, it is possible to argue that appropriate numerical schemes cannot arise directly from those derived from the simplest homogeneous case without source terms. New solutions are presented in this work by defining weak solutions that include the presence of source terms. To do that, the solvers presented in this work extend the number of waves in the well known HLL and HLLC solvers involving a stationary jump in the solution. This is done without modifying the original solution vector of conserved quantities. The resulting approximate Riemann solvers include variable bed level surface and friction. Solvers are systematically assessed via a series of test problems with exact solutions for one and two dimensions, including steady and unsteady flow configurations, variation of the flooded area in time and comparisons with experimental data. The obtained results point out that the new method is able to predict faithfully the overall behavior of the solution and of any type of waves.     

Spin particles at stratified media: operator approach

The operator formalism of quantum mechanics is applied to the problem of reflection and transmission of non-relativistic spin particles at stratified media. Two basic numerical methods in optics of stratified media, the matrix method of Abeles and the formalism of Airy, have been thus generalized for non-relativistic spin particles. Such an approach provides numerical solution of the problem of interaction of a spin particle in an arbitrary state with a spin-dependent one-dimensional potential. Application of the generalized Airy's formalism to neutrons in magnetically non-collinear stratified media has been considered as an example.     

Effects of nonlinear wave coupling: Accelerated solitons

Boomerons are described as accelerated solitons for special integrable systems of coupled wave equations. A general formalism based on the Lax pair method is set up to introduce such systems which look of Nonlinear Schr?dinger-type with linear, quadratic and cubic coupling terms. The one-soliton solution of such general systems is also briefly discussed. We display special instances of wave systems which are of potential interest for applications, including dispersion-less models of resonating waves. Among these, special attention and details are given to the celebrated equations describing the resonant interaction of three waves, in view of their application to optical pulse propagation in quadratic nonlinear media. For this particular case, we present exact solutions of the three-wave resonant interaction system, in the form of triplets moving with a common nonlinear velocity (simultons). The simultons have nontrivial phase-fronts and exist for different velocities and energy flows. We studied simulton stability upon propagation, and found that solitons with a velocity greater than a certain critical value are stable. We explore a novel consequence of the particle-like nature of three-wave simultons, namely their inelastic scattering with particular linear waves. Such phenomenon is associated with the excitation (decay) of stable (unstable) simultons by means of the absorption (emission) of the energy carried by a particular isolated pulse. Inelastic processes are exactly described in terms of boomerons. We also briefly consider collisions between different three-wave simultons.     

Simulation of Vortex Convection in a Compressible Viscous Flow with Dynamic Mesh Adaptation

In this work, vortex convection is simulated using a dynamic mesh adaptation procedure. In each adaptation period, the mesh is refined in the regions where the phenomena evolve and is coarsened in the regions where the phenomena deviate since the last adaptation. A simple indicator of mesh adaptation that accounts for the solution progression is defined. The generation of dynamic adaptive meshes is based on multilevel refinement/coarsening. The efficiency and accuracy of the present procedure are validated by simulating vortex convection in a uniform flow. Two unsteady compressible turbulent flows involving blade-vortex interactions are investigated to demonstrate further the applicability of the procedure. Computed results agree well with the published experimental data or numerical results.     

Padé–Legendre approximants for uncertainty analysis with discontinuous response surfaces

A novel uncertainty propagation method for problems characterized by highly non-linear or discontinuous system responses is presented. The approach is based on a Padé–Legendre (PL) formalism which does not require modifications to existing computational tools (non-intrusive approach) and it is a global method. The paper presents a novel PL method for problems in multiple dimensions, which is non-trivial in the Padé literature. In addition, a filtering procedure is developed in order to minimize the errors introduced in the approximation close to the discontinuities. The numerical examples include fluid dynamic problems characterized by shock waves: a simple dual throat nozzle problem with uncertain initial state, and the turbulent transonic flow over a transonic airfoil where the flight conditions are assumed to be uncertain. Results are presented in terms of statistics of both shock position and strength and are compared to Monte Carlo simulations.     

Computation of Current Cumulants for Small Nonequilibrium Systems

We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on identifying the current cumulants from a Rayleigh-Schrödinger perturbation expansion for the generating function. Here it is derived from a simple path-distribution identity and extended to the joint statistics of multiple currents. For a possible thermodynamical interpretation, we compare this approach to a generalized Onsager-Machlup formalism. We present calculations for a boundary driven Kawasaki dynamics on a one-dimensional chain, both for attractive and repulsive particle interactions.     

Diffuse optical tomography of dynamic inhomogeneities in randomly inhomogeneous media

The transport of the time autocorrelation function in randomly inhomogeneous media with spatially separated static and dynamic regions is considered. Combining the photon mean trajectory method with the diffusing-wave spectroscopy technique, a method is proposed for fast reconstruction of images of dynamic inhomogeneities in a randomly inhomogeneous medium with a specified dynamics of scatterers, including media with Brownian diffusion and directional flows. The method of mean trajectories is complemented by Monte Carlo modeling, which makes it possible to apply this method to systems with a complex dynamics of scatters.     

Coherent transport in a periodically driven bistable system

The quantum dynamics of a quartic double well, subjected to a harmonically oscillating field, is studied in the framework of the Floquet formalism. The modifications of the familiar tunneling process due to the driving are investigated numerically and explained in terms of the structure of the corresponding local quasienergy spectrum. In particular, there is a one-dimensional manifold in the parameter space spanned by the amplitude and frequency of the driving force, where tunneling is almost completely suppressed by the coherent driving. The quantal dynamics in the semiclassical regime as well as the influence of weak incoherent processes are briefly discussed.     

Spectral Green's Functions for Layered Gyrotropic Structures Through a Transmission-Line Approach

In this work, a straightforward method is shown to derive spectral Green's functions in classes of planar structures including gyrotropic media, based on a recently proposed transmission-line formalism. In particular, the analysis is expressly carried out for a current line source in layered configurations with transversely-magnetized ferrites, useful for microwave and millimeter-wave waveguiding and radiating devices.     

Response of finite many-electron systems beyond the time-dependent local density approximation: Application to small metal clusters

A linear response formalism is developed which is based on density functional theory within the local density approximation, but which is now corrected for its spurious self-interaction errors, in the way originally proposed by Perdew and Zunger for ground state calculations. The original formulation is extended to incorporate self-interaction corrections in the scrrening terms. The general formalism is then applied to the calculation of the static and dynamic response of the metal clusters {Na₈, Na₉⁺}, {Na₂₀, Na} and {Na₄₀ Na} within the jellium model. Comparison with experimental data and with other theoretical calculations indicates that the present formalism accounts for the overall (and most of the fine) features of the photoabsorption spectrum of these systems, providing a systematic improvement with respect to previous approaches. The remaining discrepancies are rationalized in terms of the effects to be expected by correctly accounting for the discrete structure of the ionic cores.